
Time  Reversal Invariance Test at COSY 
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The TRICexperiment is planned as a novel highprecision test of
timereversal invariance, which conserves_{ } parity. Using the internal
circulating polarized proton beam of the COSYring at the
Forschungszentrum Jülich and a tensor polarized
atomicbeam target, the total crosssection asymmetry A_{
y,xz } is to be measured with an accuracy of
10^{6}. The general ideas of this measurement are described
in the Proposal "Test of TimeReversal Invariance in ProtonDeuteron
Scattering" (Proposal I ).^{ }

Test of TimeReversal Invariance
in ProtonDeuteron Scattering
Proposal by:
P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst
Institut für Strahlen und Kernphysik der Universität Bonn, Germany
J. Dietrich, O. Felden, R, Gebel, M. Glende
Institut für Kernphysik, Forschungszentrum Jülich, Germany
H. E. Conzett
Lawrence Berkeley Laboratory, Berkeley, USA
M. Beyer
Institut für Theoretische Kernphysik der Universität Bonn, Germany
H. Paetz gen. Schieck
Institut für Kernphysik der Universität Köln, Germany
W. Kretschmer
Physikalisches Institut der Universität Erlangen, Germany
We propose to perform a novel (Peven, Todd) null test of timereversal invariance to an accuracy of 10^{4} (Phase 1) or 10^{6} (Phase 2). The parity conserving timereversal violating observable is the total crosssection^{ } asymmetry A_{y,xz}. The measurement is planned as an internal target transmission experiment^{ } at the cooler synchrotron COSY. A_{y,xz} is measured using a polarized^{ } beam with an energy above 1 GeV and a tensor polarized deuteron^{ } target.
So far, the only link to a violation of timereversal symmetry is given via the CPTtheorem and the observation of CPviolation in the neutral kaon system. Although the CPviolation could be accomodated by a complex phase of the Kobayashi Maskawamatrix^{1)} or the thetaterm^{2)} allowed by QCD, other explanations go beyond the standard model, like for instance the extension of the Higgs sector^{3)}, the superweak interaction^{4)}, or the leftright symmetric models^{5)}. These extensions of the standard model may lead to interactions^{ } that are not related to the observed CP or Tviolation. Since the origin of the CP or Tviolation is not clear, further experimental^{ } tests of CP or Tinvariance outside the kaon system are necessary to probe the manifestation of the interaction responsible^{ } for the observed or possible new CPviolating effects.
In this context more direct information is expected from tests involving elementary particles compared to tests involving complex nuclei. In addition, we intend to probe the timereversal invariance with parity being conserved in contrast to experiments which test parity and time reversal invariance (TRI) simultaneously (cf. tests of the electricdipole moment of elementary particles).
Usually Peven TRI tests compare two observables (cf. tests of detailed balance or P A tests). Since in these experiments two observables have to be compared, the experimental accuracy^{6)} was limited to 10^{3}  10^{2}. The accuracy can be increased by orders of magnitude if a true null^{ } experiment is performed i.e. a nonvanishing value of one single observable proves that the symmetry involved is violated. An example of this kind^{ } of experiment is the measurement of the parity violating quantity A_{z} in protonproton scattering^{7)}, which has been measured to some 10^{8} (cf. Table 1). In this context the term “true” stresses the concept that the intended test has to be completely independent^{ } from dynamical assumtions. Therefore, the interpretation of the result is neither restricted nor subject to: Final state interactions,^{ } special tensorial interactions or, Hamiltonians of a certain form. True null tests are based only on the structure of the scattering matrix as determined by general conservation laws^{8)}.
It has been proven^{8)} that there exists no true null test of TRI in a nuclear reaction with two particles in and two particles out, except for forward scattering. Based on this exception, Conzett^{9)} could show that a transmission experiment can be devised, which constitutes a true TRI null test. He suggested to measure^{ } the total crosssection asymmetry A_{y,xz} of vector polarized spin 1/2 particles interacting with tensor^{ } polarized spin 1 particles.
We intend to study this observable A_{y,xz} in the protondeuteron system with the proton polarization P_{y} along the y direction and the deuteron tensor polarization P_{xz} aligned along the x=z direction. The protondeuteron system has the advantage of being a particularly simple system allowing still a direct analysis in terms of timereversal violating (TRV) nucleonnucleon potentials based e.g. on one meson exchange. In addition, the protondeuteron system offers the opportunity to test simultaneously the pp and the pn interaction. According to a theorem of Simonius^{10)}, the np system is favoured over the pp system as a TRI testing ground in view of the symmetry restrictions^{ } on possible TRV meson exchange processes. In principle, both systems can be tested with the intended^{ } experiment.
Table 1
Comparison of accuracies of TRI and Parityviolation tests




































We intend to study the TRV quantity A_{y,xz} in a transmission experiment using an internal deuteron target in the cooler synchrotron COSY. The tensor polarized deuteron target is prepared using the polarized atomic beam target facility of the COSY experiment #5 (phase 1). Phase 2 is characterized by an improved control of systematic error contributions and the addition of a target cell to the polarized atomic beam target. The transmission losses of the circulating polarized proton beam are measured with high precision as a function of the vector and tensorpolarization P_{y} and P_{xz}, respectively. Thus, for this experiment the COSY facility is not only used as an accelerator, but also as an ideal forward spectrometer and detector.
A transmission experiment involving polarized particles is described by the generalized optical theorem^{18)} :








The density matrix reflects the experimental setup, whereas the scattering matrix F(0) of the forward scattering amplitudes contains the physics, which is to be tested. In the following it is shown which observable conserves parity but violates timereversal and that the time reversed situation is tested by flipping the spin.
The discussion of parity conserving (Peven) TRV (Todd) observable follows the arguments of Ohlsen^{19)}. It is discussed in the projectile helicity frame i.e.:
e_{z} = e_{kin}
with:
e is a unit vector pointing in the direction of x, y, z, kin
and kout
(2)
e_{y} = e_{kin} x e_{kout}
e_{x} = e_{y} x e_{z}
Since for a transmission experiment e_{kout} is parallel to e_{kin}, the direction of e_{y} can be chosen at will. A convenient choice is to have e_{y} parallel to the proton polarization P_{y}.
In general a polarization observable describing a process of two particles having tensor polarizations of ranks r and r´ is characterized by a quantity with a number n_{r} of indices with: n_{r} = r_{in} + r´_{in} + r_{out} + r´_{out}. Each index specifies whether the polarization is observed in x, y, zdirection or not at all (index=0).
For the intended transmission experiment only the initial states are of interest, thus: n_{r} = r_{in} + r´_{in}. Furthermore, the quantity of interest has to be invariant under the rotation about the zaxis (R_{z}even). R_{z} invariance means to have an observable that behaves odd or even as a function of the scattering angle theta. Equivalent to this condition behaves the sum of the indices n_{x}+n_{y}, which is odd or even, respectively. All "odd" quantities with this respect rule out to the degree that the acceptance angle of the detector (i.e. COSY) is small. Since COSY can be tuned to have a small acceptance angle without a significant loss in luminosity, a decisive advantage over an external (spectrometer) experiment is given.
According to Ohlsen^{19)}, the symmetry character of a polarization amplitude with n_{r} = n_{x}+n_{y}+n_{z} indices can be determined by "counting rules". n_{x} , n_{y }, and n_{z} are the numbers of x, y, and z indices of the observable in question. In detail the following counting rules apply for a Peven, Todd, and R_{z}even quantity:
Parity conservation : n_{x}+ n_{z} has to be even (3)
R_{z} invariance : n_{x}+ n_{y} has to be even
The minimal configuration fulfilling these conditions gives:





internal target with the thickness d and density rho 


For the case of polarized particles _{T}
has to be replaced by:



outside of the target 






In order to measure A_{y,xz} the transmission asymmetry T_{y,xz} is introduced:

P_{y} > 0, P_{xz} > 0 

i.e. either P_{y} < 0 , P_{xz} < 0 

with respect to the protondeuteron spinalignment 
this gives:
Is the argument of the tanh in equation (8) small, then:
With the help of equation (9) the total crosssection asymmetry A_{y,xz} can be determined.








Basically, the experimental setup only needs equipment that is provided for other experiments, i.e. a polarized proton beam in COSY, an atomic beam source producing polarized protons and deuterons for internal target experiments, and an online current monitor^{20)} of high precision that is a standard diagnosis device for the operation of COSY.
A typical measurement sequence may be:








In _{ } the following, an upper limit of the accuracy that can be achieved is estimated from the shot noise of the scattered particles. For a two weeks run the beam is assumed to be on target for 10 days. With an unpolarized crosssection _{o} = 80 mb the following accuracies for various beam intensities and target thicknesses are calculated (Table 2):
Table 2
Accuracy of this experiment calculated from basic statistics for
phase 1 (rho· d = 10^{12 }atoms/cm^{2}) and phase 2
(rho·d = 4·10^{14 }atoms/cm^{2})
















For a conservative estimation of the accuracy that can be achieved, the sensitivity S is introduced in equation (9):
Equation (10) defines S:
With a spinflip every 5 s and with:








S becomes: S = 2.4 · 10^{4}.
The precision of the transmission asymmetry _{} T_{y,xz} is calculated from the precision of the current measurement. For 1.3 · 10^{11} protons in the COSY^{ } ring the current is measured within 40 ms to a precision of 5 · 10^{5}. Within 10_{ } days the precision of the transmission asymmetry _{} T_{y,xz} is measured to 1 ·10^{8}. With equation (10) the accuracy delta A_{y,xz }of the totalcrosssection asymmetry A_{y,xz} is calculated: delta ^{ }A_{y,xz} = 4 ·10^{5}.
The accuracy of A_{y,xz} can be further improved by increasing the sensitivity S or by improving the precision of the _{} T_{y,xz} measurement. The sensitivity can be improved^{ } by extending the spinflip period, for instance from 5s to 50s. As a consequence the number of turns N and hence the sensitivity S is increased^{ } by an order of magnitude. In case the precision of the current measurement is improved simultaneously by an order of magnitude the precision of _{} T_{y,xz} is improved accordingly, and delta A_{y,xz} reduces to 4·10^{7}. Under these conditions delta A_{y,xz} is dominated by the shot noise of the underlying statistics of the scattering process, and it becomes increasingly important to discuss in more^{ } detail the handling of systematic errors.
Two obvious experimental effects are discussed: i) the loss of the beam intensity somewhere in the ring except in the target zone, and ii) competing polarization observables.




If A_{y,xz} is calculated from changing the proton polarization each time the ring is filled, all observables of Table 3 in line 1 and 5 cancel. Since only the proton polarization P_{y} is an eigenvector in the ring, all observables with respect to the proton polarization P_{x} and P_{z} cancel too (the average of P_{x} and P_{z} should be < 10^{8} in a 10 days run). This is true for lines 2, 4, 6, and 8 in Table 3.
In the remaining lines 3 and 7 of Table 3 all quantities with a hat cancel, because they are not R_{z}even (n_{x}+n_{y} has to be even). A_{y,x} and A_{y,yz} violate parity conservation (n_{x}+n_{z} is odd for these quantities). Therefore, since p  d scattering is an elementary process, these quantities are expected to be of the order of 10^{7}, even if parity is violated. Thus, besides our quantity of interest A_{y,xz}, only A_{y,y} "survives ".
Table 3
Polarization observables of the total crosssection in pd scattering.
The first index refers to the proton polarization, the second and third index refers to the
deuteron vector and tensor polarisation.



























All quantities with a hat cancel, since they are R_{z}odd (n_{x}+n_{y} has to be even).
The latter quantity is small, because i) there must be a deuteron vector polarization in the first place, and ii) there must be a misalignment between the COSY beam direction and the deuteron beam, so that a deuteron vector polarization is able to generate a P_{y} deuteron vector polarization. The deuteron vector polarization can be adjusted to be zero in the atomic beam source, if this polarization is measured in the dump of the atomic beam source. The quality by which this is done makes the difference between phase 1 and phase 2 of this experiment.
Without major effort (phase 1), the deuteron polarization P_{z} can be limited to a few percent. The deuteron source and the proton beam can be aligned to better than 0.1^{o}, resulting in a false deuteron polarization P_{y} < 10^{4}, which limits the accuracy attainable in phase 1 of the experiment.
The deuteron vector and tensorpolarization can for instance be measured in a scattering experiment via the d+d reaction^{21)} at 30 keV or rather by measuring the change of the atomic beam intensity with the aid of a quadrupolemassspectrometer. In this case the deuteron beam dump has to be replaced by an arrangement of two 6pole magnets and at least two RFtransitions (principle of an "inverted" nuclear spinpreparation system of a groundstate atomic beam source). Alternatively, a spinfilter can be used, which is essentially the spinpreparation module of a Lambshift source. The installation of either of these three methods provides a precise determination of the deuteron vector and tensorpolarization and is mandatory for phase 2 of the proposed experiment.
The precision of the standard COSY current monitors can be improved for our purpose by an order of magnitude^{22)}, which would improve the precision of the transmission asymmetry _{} T_{y,xz} measurement accordingly. The precision of the standard COSY current monitors is limited by the Barkhausen noise of its ferrits. Using the fast pickup devices of the stochastic cooler tanks of COSY with its cooled FETamplifiers provides lower noise current monitors. Moreover, because there are several such devices placed about the COSY ring, the precision of the current measurement can be improved further.
Even without these improvement the quantity of interest A_{y,xz} can be measured in phase 1 and phase 2 to an accuracy of 10^{4} and some 10^{6}, respectively. The accuracy of this novel Peven, Todd true null test of timereversal invariance is neither limited by the available statistics nor the precision that can be achieved, rather than by systematic error contributions^{ }. Below an accuracy of 10^{6} special attention has to be payed to systematic error contributions of observables^{ } that are sensitive to parity violation.
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Proposal for
Measurement
of the Total _{
}
Correlation Coefficient A_{y,y}
by the TRIC Collaboration
In view of the proposed Test of TimeReversal Invariance (TRI) in ProtonDeuteron Scattering [18] at COSY (proposal #22) the measurement of the dominant error contributions is decisive for the accuracy of the TRI experiment. In the TRI proposal it is argued that the total correlation coefficient A_{y,y} is the only observable in protondeuteron scattering, which can fake a TRI effect.
Since the total correlation coefficient A_{y,y} is not known at 1 GeV which is the proposed energy for the TRI test A_{y,y} has to be determined. The experiment is to take place at TP2 and thus the EDDA detector can be used as an internal polarimeter. A_{y,y} shall be measured in two ways:
i) The circulating polarized proton beam at 1 GeV interacts with the polarized deuteron beam from the atomicbeam target for EDDA [6,9]. Asymmetries with respect to the spin configuration of the beam and the target are measured over the total angular acceptance of the EDDA detector.
ii) The measurement is performed by observing the decrease of the circulating current in COSY as a function of the spin alignments of the beam and the target (this method is described in detail in the TRI proposal #22 [1])
Method i) is very useful for studying systematic errors of the measuring principle. Since the angular acceptance of the EDDA detector does not cover completely 180^{o} and the elastic channel is preferentially analysed, A_{y,y} is only approximately determined.
In contrast, method ii) measures all inelastic channels and regards the complete angular range from 0^{o}180^{o}, since the forward scattering amplitude is measured via the transmission asymmetry _{ }T_{y,y}. _{ }T_{y,y} contains A_{y,y}, the quantity of interest for this experiment in the same way as T_{y,xz} contains A_{y,xz}, the quantity of interest for the TRI test (cf. the TRI proposal^{ }). Thus a novel type of internal experiment will be established that utilizes the COSY ring not only as an accelerator but also as an ideal^{ } forward spectrometer and detector.
The apparatus for method i) is the usual EDDA setup with a special RFtransition for the polarized atomicbeam target, which provides a vector polarized deuteron beam (P_{z} = 1) This transition has been developed in the diploma thesis of Dirk Lorenser, University Bonn. Since only weak holding fields across the interaction zone are allowed at COSY, a pure deuteron state has to be prepared. This in turn implies that simultaneously the atomic deuteron beam will be tensor polarized (P_{zz} = 1). On the other hand, switching off the RFtransitions provides a deuteron beam with P_{z} = 1/3 and P_{zz} = –1/3 at the exit of the target. The holding field is vertically aligned so that the vector and tensoralignment is adiabatically changed to P_{y} and P_{yy} at the interaction zone.
Since the holding field is provided by ferrite cored electric magnets, a fast spinflip (< 1ms) can be provided. Switching off the RFtransition gives a different linear combination of deuteron vector and tensorpolarization. Finally, interspersing sequences with an unpolarized proton beam, allows to extract A_{y,y}. In more detail, according to Ohlsen [10], for a vertical holding field, the following quantities are of interest:
_{} (1)
with:
If the LeftRight asymmetries are not measured with the EDDA detector, all underlined quantities do not contribute. Providing an unpolarized proton beam with the flipping of the holding field and the RFtransition switched on and off, allows to determine A_{yy} and _{ } . Then, with a polarized proton beam, A_{y,y} the quantity of interest^{ } can be determined as soon as the proton spin is flipped.
Since for method i) it has been shown that by proper combinations of spin flip and switching on and off the RFtransition the total amount of scattered particles is changed, the transmission is changed accordingly. Therefore,^{ } A_{y,y} can be deduced from a transmission asymmetry too.
Given a crosssection of 80 mb, a target density of 2·10^{11} deuterons/cm^{2}, an intensity of 10^{10} polarized protons circulating at 1 MHz, results in a total rate of 160 Hz. Under these conditions for the scattering experiments^{ } some hours should be sufficient for a precision of some percent.^{ }
The TRIC collaboration is asking for 6 days of beamtime splitted in 2 periods of 3 days each. These periods should preferably be scheduled following a beam development week. The time is intended for the following purposes:^{ }
Especially: a) Study the quality of the deuteron polarization.
b) Study the quality of the polarized proton beam
c) Study systematic error sources
2) Establish a novel measuring technique for a ringaccelerator. Use the EDDA detector as an efficient polarimeter and luminosity monitor.
1) COSY Proposal #22: “Test of TimeReversal Invariance in ProtonDeuteron Scattering”
2) P.D. Eversheim
Proc. of the 2nd Adriatico Research Conf. on Pol. Dynamics in Nuclear and Particle Phys., Triest, Italy, World Scientific (1992) 142
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4) P.D. Eversheim
Int. Workshop on Pol. Beams and Pol. Gas Targets, Cologne, Germany
World Scientific (1996) 224
5) P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst, M. Beyer, H. Paetz gen. Schieck, W. Kretschmer and H.E. Conzett
12^{th} Int. Symp. on HighEnergy Physics, Amsterdam, The Netherlands
World Scientific (1996) 303
6) P.D. Eversheim, M. Altmeier, and O. Felden
Nucl. Phys. A626 (1997) 117c
7) P.D. Eversheim, F. Hinterberger, J. Bisplinghoff, R. Jahn, J. Ernst, H. Paetz gen. Schieck, W. Kretschmer, and H.E. Conzett
AIP Conference Proceedings 421 (1997) 501
8) P.D. Eversheim
Nucl. Phys. A629 (1998) 471c
9) P.D. Eversheim, M. Altmeier, O.Felden, M. Glende, M. Walker, A. Hiemer, and R. Gebel
AIP Conference Proceedings 421 (1997) 419
10) G.G. Ohlsen
Rep.Prog.Phys. 35 (1972) 760


